The Electron Microscope as a Structure Projector

Abstract

The intuitive understanding of the process of 3D reconstruction is based on a number of assumptions, which are easily made unconsciously; the most crucial is the belief that what is detected is some kind of projection through the structure. This ‘projection’ need not necessarily be a (weighted) sum or integral through the structure of some physical property of the latter; in principle, a monotonically varying function would be acceptable, although solving the corresponding inverse problem might not be easy. In practice, however, the usual interpretation of ‘projection’ is overwhelmingly adopted, and it was for this definition that Radon (1917) first proposed a solution. In the case of light shone through a translucent structure of varying opacity, a 3D transparency as it were, the validity of this projection assumption seems too obvious to need discussion. We know enough about the behavior of X-rays in matter to establish the conditions in which it is valid in radiography. In this chapter, we enquire whether it is valid in electron microscopy, where intuition might well lead us to suspect that it is not. Electron-specimen interactions are very different from those encountered in X-ray tomography; the specimens are themselves very different in nature, creating phase rather than amplitude contrast, and an optical system is needed to transform the information about the specimen that the electrons have acquired into a visible image.